This is problem can be solved relatively by using a Brute Force technique, that is to say trying lots of combinations. There are some things you can do to speed up your working….

We can have a maximum of 10 horses or we would have no money left.

We can have a maximum of 12 bunches of ducks or we would have too many animals.

A spread sheet might help

However there is a more eloquent approach (thanks to Gary Short):

This can be solved as a simultaneous equation, with three variables and two equation…

Our equations are:

10*H + G + D/8 = 100 (pounds)

H + G + D = 100 (animals)

Subtracting equation II from equation I gives:

9H – 7D/8 = 0
OR….
9H = 7D/8

(at this point we can actually stop solving the equation as we know that ducks come in bunches of 8 so the feature D/8 in the equation actually represents the number of bunches of duck, therefore the equation is simply 9H = 7DB which easily gives us a solution. But we will continue….)

72H = 7D

Directly this equation is unsolvable as there are an infinite number of solutions. However, we have the restraint that both variables must be integers and that there H<100 & D<100.